Kinematics of shear bands

Shear bands appear at limit states of soil bodies. They are analysed as thin zones of localised deformation that takes place as simple (i.e. dilatant) shear. It can be observed, however, that shear bands are discontinuous and also may be “reflected” at rigid boundaries. These phenomena appear as incompatible with the assumed shear deformation. The analysis in this paper reveals the kinematics of such “incompatibilities” in terms of continuous deformation fields.     

Relation between mean stress,thermodynamic, and lithostatic pressure

Pressure is one of the most important parameters to be quantified in geological problems. However, in metamorphic systems the pressure is usually calculated with two different approaches. One pressure calculation is based on petrological phase equilibria and this pressure is often termed thermodynamic pressure. The other calculation is based on continuum mechanics, which provides a mean stress that is commonly used to estimate the thermodynamic pressure. Both thermodynamic pressure calculations can be justified by the accuracy and applicability of the results. Here, we consider systems with low‐differential stress (<1 kbar) and no irreversible volumetric deformation, and refer to them as conventional systems. We investigate the relationship between mean stress and thermodynamic pressure. We discuss the meaning of thermodynamic pressure and its calculation for irreversible processes such as viscous deformation and heat conduction, which exhibit entropy production. Moreover, it is demonstrated that the mean stress for incompressible viscous deformation is essentially equal to the mean stress for the corresponding viscous deformation with elastic compressibility, if the characteristic time of deformation is five times longer than the Maxwell viscoelastic relaxation time that is equal to the ratio of shear viscosity to bulk modulus. For typical lithospheric rocks, this Maxwell time is smaller than c. 10,000 years. Therefore, numerical simulations of long‐term (>10 kyr) geodynamic processes, employing incompressible deformation, provide mean stress values that are close to the mean‐stress value associated with elastic compressibility. Finally, we show that for conventional systems the mean stress is essentially equal to the thermodynamic pressure. However, mean stress and, hence, thermodynamic pressure can be significantly different from the lithostatic pressure.     

Erratum to: Geotechnical and mineralogical properties of weak rocks from Central Greece

The original version of this article was published in Central European Journal of Geosciences volume 1, issue 4 (2009), pp 431–442, DOI:10.2478/v10085-009-0029-0. Unfortunately the original version of this article contains mistakes in authors names which we correct here. Editorial staff of the journal apologise for any inconvenience that may result from the oversight.     

Derivation of new SAC/FEMA performance evaluation solutions with second‐order hazard approximation

A novel set of SAC/FEMA‐style closed‐form expressions is presented to accurately assess structural safety under seismic action. Such solutions allow the practical evaluation of the risk integral convolving seismic hazard and structural response by using a number of idealizations to achieve a simple analytical form. The most heavily criticized approximation of the SAC/FEMA formats is the first‐order power‐law fit of the hazard curve. It results to unacceptable errors whenever the curvature of the hazard function becomes significant. Adopting a second‐order fit, instead, allows capturing the hazard curvature at the cost of necessitating new analytic forms. The new set of equations is a complete replacement of the original, enabling (a) accurate estimation of the mean annual frequency of limit‐state exceedance and (b) safety checking for specified performance objectives in a code‐compatible format. More importantly, the flexibility of higher‐order fitting guarantees a wider‐range validity of the local hazard approximation. Thus, it enables the inversion of the formulas for practically estimating the allowable demand or the required capacity to fulfill any design objective. Copyright © 2012 John Wiley & Sons, Ltd.     

Development of collapse-consistent loading protocols for experimental testing of steel columns

In order to effectively utilize results from quasi-static cyclic testing on structural components for the earthquake-induced collapse risk quantification of structures, the need exists to establish collapse-consistent loading protocols representing the asymmetric lateral drift demands of structures under low-probability of occurrence earthquakes. This paper summarizes the development of such protocols for experimental testing of steel columns prone to inelastic local buckling. The protocols are fully defined with a deformation- and a force-controlled parameter. They are generally applicable to quantify the capacity and demands of steel columns experiencing constant and variable axial load coupled with lateral drift demands. Through rigorous nonlinear earthquake collapse simulations, it is found that the building height, the column's local slenderness ratio, and ground motion type have the largest influence on the dual-parameter loading protocol indexes. Comprehensive comparisons with measured data from full-scale shake table collapse tests suggest that unlike routinely used symmetric cyclic loading histories, the proposed loading protocol provides sufficient information for modeling strength and stiffness deterioration in steel columns at large inelastic deformations.     

Historical seismicity, palaeoseismicity and seismic risk in Western Macedonia, Northern Greece

Western Macedonia, Northern Greece, was a seismically quiescent region for one or more centuries, and was regarded as a nearly aseismic, rigid block inside a broad zone of distributed continental deformation and faulting, and a region of minimum seismic risk. Consequently, the May 13, 1995 destructive earthquake (M = 6.6) which hit this assumed aseismic zone was a surprise for scientists, government and population.However, historical and archaeoseismic evidence, as well as coastal change data indicate that the assumed aseismic region of Western Macedonia has been affected in the last 2,000 years by at least seven, and possibly nine destructive earthquakes. One of these earthquakes occurred in circa 1700, and probably had the same epicentre with, but higher magnitude than the 1995 shock.The earthquake in circa 1700 is deduced from historical data and is modelled on the base of a swarm of church repairs which is explained as post-seismic recovery of the broader Kozani area: except for certain well known cases of towns or areas in which religious privileges were granted, large scale repairs or reconstruction of churches during the Ottoman period were possible only after Sultan's permissions, usually following earthquakes and other calamities.It can hence be concluded that some, at least, of the apparently aseismic regions inside broad zones of distributed seismicity are hit by stronger shocks, but with longer (200 years or more) recurrence intervals than their adjacent zones. Consequently, the seismic risk of the apparently aseismic regions is certainly not low, especially since relatively long periods of seismic quiescence lead to constructions vulnerable to earthquakes.     

Pulse-like versus non-pulse-like ground motion records: Spectral shape comparisons and record selection strategies

Pulse-like records are well recognized for their potential to impose higher demands on structures when compared with ordinary records. The increased severity of the structural response usually caused by pulse-like records is commonly attributed to the spectral increment around the pulse period. By comparing the building response to sets of spectrally equivalent pulse-like and ordinary records, we show that there are characteristics of pulse-like records beyond the shape of the acceleration response spectrum that affect the results of nonlinear dynamic analysis. Nevertheless, spectral shape together with the ratio of pulse period to the first-mode structural period, T_p/T₁, are confirmed as “sufficient” predictors for deformation and acceleration response metrics in a building, conditioned on the seismic intensity. Furthermore, the average spectral acceleration over a period range, AvgSA, is shown to incorporate to a good proxy for spectral shape, and together with T_p/T₁, form an efficient and sufficient intensity measure for response prediction to pulse-like ground motions. Following this latter route, we propose a record selection scheme that maintains the consistency of T_p with the hazard of the site but uses AvgSA to account for the response sensitivity to spectral shape.     

Imaging Pathways in Fractured Rock Using Three‐Dimensional Electrical Resistivity Tomography

Major challenges exist in delineating bedrock fracture zones because these cause abrupt changes in geological and hydrogeological properties over small distances. Borehole observations cannot sufficiently capture heterogeneity in these systems. Geophysical techniques offer the potential to image properties and processes in between boreholes. We used three‐dimensional cross borehole electrical resistivity tomography (ERT) in a 9 m (diameter) × 15 m well field to capture high‐resolution flow and transport processes in a fractured mudstone contaminated by chlorinated solvents, primarily trichloroethylene. Conductive (sodium bromide) and resistive (deionized water) injections were monitored in seven boreholes. Electrode arrays with isolation packers and fluid sampling ports were designed to enable acquisition of ERT measurements during pulsed tracer injections. Fracture zone locations and hydraulic pathways inferred from hydraulic head drawdown data were compared with electrical conductivity distributions from ERT measurements. Static ERT imaging has limited resolution to decipher individual fractures; however, these images showed alternating conductive and resistive zones, consistent with alternating laminated and massive mudstone units at the site. Tracer evolution and migration was clearly revealed in time‐lapse ERT images and supported by in situ borehole vertical apparent conductivity profiles collected during the pulsed tracer test. While water samples provided important local information at the extraction borehole, ERT delineated tracer migration over spatial scales capturing the primary hydrogeological heterogeneity controlling flow and transport. The fate of these tracer injections at this scale could not have been quantified using borehole logging and/or borehole sampling methods alone.     

Modelling of R/C members accounting for shear failure localisation: Finite element model and verification

Reinforced concrete (R/C) frame buildings designed according to older seismic codes represent a large part of the existing building stock worldwide. Their structural elements are often vulnerable to shear or flexure‐shear failure, which can eventually lead to loss of axial load resistance of vertical elements and initiate vertical progressive collapse of a building. In this study, a computationally efficient member‐type finite element model for the hysteretic response of shear critical R/C frame elements up to the onset of axial failure is presented; it accounts for shear‐flexure interaction and considers, for the first time, the localisation of shear strains, after the onset of shear failure, in a critical length defined by the diagonal failure plane. Its predictive capabilities are verified against experimental results of column and frame specimens and are shown to be accurate not only in terms of total response, but also with regard to individual deformation components. The accuracy, versatility, and simplicity of this finite element model make it a valuable tool in seismic analysis of complex R/C buildings with shear deficient structural elements.     

Modelling of R/C members accounting for shear failure localisation: Hysteretic shear model

Reinforced concrete (R/C) frame buildings designed according to older seismic codes represent a large part of the existing building stock worldwide. Their structural elements are often vulnerable to shear or flexure‐shear failure, which can eventually lead to loss of axial load resistance of vertical elements and initiate vertical progressive collapse of a building. In this study, a hysteretic model capturing the local shear response of shear‐deficient R/C elements is described in detail, with emphasis on post‐peak behaviour; it differs from existing models in that it considers the localisation of shear strains after the onset of shear failure in a critical length defined by the diagonal failure planes. Additionally, an effort is made to improve the state of the art in post‐peak shear response modelling, by compiling the largest database of experimental results for shear and flexure‐shear critical R/C columns cycled well beyond the onset of shear failure and/or up to the onset of axial failure, and developing empirical relationships for the key parameters defining the local backbone post‐peak shear response of such elements. The implementation of the derived local hysteretic shear model in a computationally efficient beam‐column finite element model with distributed shear flexibility, which accounts for all deformation types, will be presented in a companion paper.